Combining signals exhibiting multiple types of diversity

ABSTRACT

Combining signals includes receiving first signals having a first frequency and second signals having a second frequency. A first weight reflecting a signal-to-noise ratio associated with a first signal is determined for each first signal, and a first signal output is generate from the first signals in accordance with the first weights. A second weight reflecting a signal-to-noise ratio associated with a second signal is determined for each second signal, and a second signal output is generate from the second signals in accordance with the second weights. The first signal output and the second signal output are combined to yield a combined signal output.

RELATED APPLICATIONS

[0001] This application claims benefit under U.S.C. § 119(e) of U.S. Provisional Application Serial No. 60/350,188, entitled, “QUAD DIVERSITY SIGNAL IMAGE COMBINING,” filed Jan. 18, 2002.

[0002] This application is related to U.S. patent application Ser. No. 10/219,128, entitled “COMBINING SIGNAL IMAGES IN ACCORDANCE WITH SIGNAL-TO-NOISE RATIOS,” Attorney's Docket 064750.0450, filed Aug. 15, 2002.

GOVERNMENT FUNDING

[0003] The U.S. Government may have certain rights in this invention as provided for by the terms of Grant No. N00039-01-9-4003, awarded by SPAWAR of the U.S. Navy.

TECHNICAL FIELD OF THE INVENTION

[0004] This invention relates generally to communications systems, and more specifically to combining signals exhibiting multiple types of diversity.

BACKGROUND OF THE INVENTION

[0005] Signals from multiple receivers may be combined to determine content included in the signals. Known techniques for signal combining, however, may not be able to combine signals that exhibit multiple types of diversity such as temporal, frequency, polar, or spatial diversity. Consequently, known techniques for signal combining are unsatisfactory in certain situations.

SUMMARY OF THE INVENTION

[0006] In accordance with the present invention, disadvantages and problems associated with previous techniques for combining signals may be reduced or eliminated.

[0007] According to one embodiment of the present invention, combining signals includes receiving first signals having a first frequency and second signals having a second frequency. A first weight reflecting a signal-to-noise ratio associated with a first signal is determined for each first signal, and a first signal output is generate from the first signals in accordance with the first weights. A second weight reflecting a signal-to-noise ratio associated with a second signal is determined for each second signal, and a second signal output is generate from the second signals in accordance with the second weights. The first signal output and the second signal output are combined to yield a combined signal output.

[0008] Certain embodiments of the invention may provide one or more technical advantages. A technical advantage of one embodiment may be that signals are combined in accordance with the signal-to-noise ratios associated with the signals, such that maximal ratio combining gain may be substantially realized. Accordingly, signals that exhibit multiple types of diversity such as temporal, frequency, polar, or spatial diversity may be combined.

[0009] Certain embodiments of the invention may include none, some, or all of the above technical advantages. One or more other technical advantages may be readily apparent to one skilled in the art from the figures, descriptions, and claims included herein.

BRIEF DESCRIPTION OF THE DRAWINGS

[0010] For a more complete understanding of the present invention and the advantages thereof, reference is now made to the following description taken in conjunction with the accompanying drawings.

[0011]FIG. 1 is a block diagram of one embodiment of a system for combining signals;

[0012]FIG. 2 is a block diagram of one embodiment of an interpolator of the system of FIG. 1;

[0013]FIG. 3 is a block diagram of one embodiment of a system that includes phase aligners and magnitude estimators;

[0014]FIG. 4 is a block diagram of one embodiment of a reference constructor of the system of FIG. 1; and

[0015]FIG. 5 is a block diagram of one embodiment of coordinating modules of the system of FIG. 1.

DETAILED DESCRIPTION OF THE DRAWINGS

[0016] The invention and its advantages are best understood by referring to FIGS. 1 through 5 of the drawings, like numerals being used for like and corresponding parts of the various drawings.

[0017]FIG. 1 is a block diagram of one embodiment of a system 10 for combining signals. System 10 may be used to combine signals in accordance with signal-to-noise ratios associated with the signals, such that maximal ratio combining gain may be substantially realized. Signal-to-noise ratio weighting is insensitive to the specific cause or causes of variation of signal-to-noise ratio. Accordingly, signals that exhibit multiple types of diversity such as temporal, frequency, polar, or spatial diversity may be combined.

[0018] According to the illustrated embodiment, system 10 combines signals. The signals typically carry symbol streams, and different signals may carry substantially identical symbol streams. The signals may arrive at different times, resulting in a symbol offset among the symbols. In order to combine the signals, the signals are correlated to resolve the symbol offset. Signals may comprise, for example, phase shift keying (PSK) signals such as binary phase shift keying (BPSK) signals or staggered binary phase shift keying (SBPSK). Signals may have any suitable radio frequency and may be modulated according to any suitable modulation format.

[0019] System 10 includes antenna systems 20 a-b, frequency branches 22 a-b, a sum-weight module 26, a reference constructor 72, and coordinating modules 24 coupled as illustrated in FIG. 1. In general, antenna systems 20 a-b receive signals and separate the signals with respect to frequency. Each frequency branch 22 a receives the signals of a particular frequency and determines a signal magnitude estimate for each signal according to a signal-to-noise ratio associated with the signal. Sum-weight module 26 combines signals received from frequency branches 22 a-b according to the weights determined by frequency branches 22 a-b. Reference constructor 72 generates a correlation reference that frequency branches 22 a-b use to estimate signal magnitude. Coordinating modules 24 correlate signals of the different frequency branches 22 a-b.

[0020] According to the illustrated embodiment, an antenna system 20 a-b includes one or more antennas 30 a-b and a splitter 32 a-b. Antennas 30 a-b receive signals from one or more transmitters, and splitter 32 a-b separates the signals with respect to frequency. Antennas 30 a-b may comprise any antenna suitable for receiving signals from one or more transmitters. Antennas 30 a-b may be polarized, separated, or both. Splitter 32 a-b may comprise any device suitable for separating the signals according to frequency, and may perform other functions such as amplifying or filtering the signals.

[0021] Frequency branches 22 a-b process the signals of a specific frequency, which allows system 10 to accommodate signals exhibiting frequency diversity. In the illustrated embodiment, system 10 includes two frequency branches 22 a-b. System 10, however, may comprise any suitable number of frequency branches. A frequency branch 22 a-b may include signal branches 40 a-b, a phase aligner 42 a-b, a magnitude estimator 44 a-b, a branch combiner 45 a-b, and buffers 66 a-b and 68 coupled as shown in FIG. 1.

[0022] A signal branch 40 a-b processes signals from an antenna system 20 a-b, and includes a receiver channel 50 a-b and an interpolator 52 a-b. Receiver channel 50 a-b receives and processes signals to yield signal images. Interpolator 52 a-b applies a delay to the signals in order to compensate for symbol offsets, which may result from temporal, or spatial diversity. Accordingly, interpolator 52 a-b allows system 10 to accommodate signals exhibiting such diversity. Interpolator 52 a-b may comprise, for example, a polyphase interpolator that uses polyphase finite impulse response (FIR) structures to shift the phase of signals. A finite impulse response filter used in conjunction with a delay line may delay the signals with a phase resolution finer than one sample and allow the magnitude of the delay to vary over many symbol periods. Interpolator 52 a-b may also provide additional or other functionality such as dynamic delay control, decimation of signals, or linear-phase channel filtering. Interpolator 52 a-b is described in more detail with reference to FIG. 2. Other methods for realizing interpolation may be substituted for the polyphase filter interpolator in this invention.

[0023] Phase aligner 42 a-b aligns the phases of signals received from interpolators 52a-b of frequency branch 22 a-b. Magnitude estimator 44 a-b calculates a signal magnitude estimate for each signal that reflects a signal-to-noise ratio associated with the signal. Magnitude estimator 44 a-b is described in more detail with reference to FIG. 3. Branch combiner 45 a-b combines the signals of frequency branch 22 a-b. Buffers 66 a-b and 68 store the combined signals, and may comprise first-in-first-out buffers.

[0024] Sum-weight module 26 generates weights from the signal magnitude estimates received from magnitude estimator 44 a-b, and sums the signals according to the weights in order to generate a combined signal. The weights reflect the signal-to-noise ratios at signal branches 40 a-d. A signal-to-noise-ratio improvement may be realized if the combined signal-to-noise ratio is better than the worst individual signal-to-noise ratio of a signal branch 40 a-d. Maximal Ratio Combining performance may be substantially achieved if the signal-to-noise ratio of the combined output is better than the best individual signal's signal-to-noise ratio. Sum-weight module 26 is described in more detail with reference to FIG. 3.

[0025] Reference constructor 72 generates a correlation reference, which is used to estimate signal magnitude, from the signals at one or more frequency branches 22 a-b. Frequency branches 22 a-b may be selected in accordance with the signal energies at the frequency branches 22 a-b. For example, if frequency branch 22 a has acquired a signal, but frequency branch 22 b has not acquired a signal, the correlation reference may derived using frequency branch 22 a. A correlation reference may be derived from multiple frequency branches 22 a-b. The contribution of each frequency branch 22 a-b may be determined with respect to signal-to-noise-ratios at the frequency branches 22 a-b. A correlation reference derived from multiple frequency branches 22 a-b may be used at none, some, or all frequency branches 22 a-b. Accordingly, any number of frequency branches 22 a-b may contribute to and benefit from the correlation reference. Reference constructor 72 is described in more detail with reference to FIG. 4.

[0026] Coordinating modules 24 determine the correlation among the signals of frequency branches 22 a-b, and provide instructions to interpolators 52 a-d to align the symbols of the signals in order to correlate the signals. The signals are correlated if the symbols of the symbol streams are aligned, and are uncorrelated if the symbols are misaligned. Coordinating modules 24 include a correlation monitor 64, a correlator 62, and a symbol aligner 60.

[0027] Correlation monitor 64 monitors signal correlation and initiates correlation procedures in response to detecting signal decorrelation. Correlation monitor 64 generates correlation values that indicate positive and negative correlations among the signals. If the correlation values fail to satisfy certain threshold values, correlation monitor notifies correlator 62. Correlator 62 generates a symbol alignment tracking error, which is provided to symbol aligner 60. In response, symbol aligner 60 provides instructions to interpolators 52 to align symbols in order to correlate the signals. Coordinating modules 64 are described in more detail with reference to FIG. 5.

[0028] Modifications, additions, or omissions may be made to the system without departing from the scope of the invention. For example, system 10 may be configured to combine signals from any suitable number of antenna systems 20 at any suitable number of frequencies. For example, system 10 may be configured to combine signals from four antenna systems and at four different frequencies.

[0029] As another example, although system 10 may approximate maximal ratio combining, it is within the scope of the invention to include non-optimal weighting that may result from, for example, employing a non-optimal weight calculator. System 10 may include other compromises to optimal performance resulting from, for example, stability enhancement or single signal enhancement. Additionally, functions may be performed using any suitable logic comprising software, hardware, other logic, or any suitable combination of the preceding.

[0030]FIG. 2 is a block diagram illustrating one embodiment of interpolator 52 of system 10 of FIG. 1. Interpolator 52 provides dynamic delay compensation to equalize symbol offsets between different signals, each of which carry substantially identical symbol streams. Typically, if identical symbol streams of signals are offset in time, the time offset is equalized before combining the signals.

[0031] Interpolator 52 includes a delay line 151, tap weight coefficients 150, multipliers 152 and 154, and an adder 156. Delay line 151 stores samples of the signals received from a receiver channel 50 a-b. For example, delay line 151 may comprise a 512-word delay line that stores samples {d_(i)}, where 0≦i≦511. Delay line 151, however, may have any suitable length. Delay line 151 may be implemented using linear delay techniques or circular buffering techniques.

[0032] Tap weight coefficients 150 are used to adjust the delay applied to the samples. For example, tap weight coefficients 150 comprise tap weight coefficient sets {h_(i)(φ)} for 0≦i≦127, where φ, 0≦φ≦4, represents a phase of a finite impulse response filter. Phase φ and a pointer value τ determine the relative delay applied to the symbols streams. Initial values for phase φ and for pointer value τ may provided by symbol aligner 60, and the values of pointer value τ and phase φ may be adjusted to change the relative delay. Delay resolution may be controlled by selecting a tap weight coefficient set for an increment of the samples.

[0033] In operation, multipliers 152 and 154 multiply tap weight coefficients h_(i)(φ) with samples d_(i) to form products d_(i+τ)h_(i)(φ). Adder 156 adds the products to yield an output ${y_{n}\left( {\tau,\phi} \right)} = {\sum\limits_{i}{d_{i + \tau}{h_{i}(\phi)}}}$

[0034] that may be used to apply a delay to the samples. A processor may be used to control the operation of the elements of interpolator 52.

[0035] Modifications, additions, or omissions may be made to interpolator 52 without departing from the scope of the invention. For example, interpolator 52 may include more or fewer tap weight coefficients 150. In addition, the phase resolution of interpolator 52 may be varied to realize a specific filter response. For example, the phase resolution may be increased or decreased by increasing or decreasing the number of coefficients or the number of tap weight coefficient sets, such that a lesser or greater phase difference exists between the adjacent tap weight coefficient sets, respectively. Additionally, functions may be performed using any suitable logic comprising software, hardware, other logic, or any suitable combination of the preceding.

[0036]FIG. 3 is a block diagram of one embodiment of a system 210 that includes phase aligners 241 a-b and magnitude estimators 243 a-b. In general, system 210 correlates signal images x_(i)(t) with a correlation reference y′(t) to yield phasors r_(i), and generates signal magnitude estimates M_(i) from the phasors r_(i). Weights W_(i) of signal images x_(i)(t) are determined from the signal magnitude estimates M_(i). Each weight W_(i) reflects the signal-to-noise ratio associated with the corresponding signal image x_(i)(t). “Each” as used in this document refers to each member of a set or each member of a subset of the set. The phase of unity magnitude phasors R_(i) that substantially track the phases of phasors r_(i) are applied to signal images x_(i)(t) to yield phase-aligned signal images Rx_(i)(t) that are substantially phase aligned.

[0037] Weights W_(i) are applied to phase-aligned signal images Rx_(i)(t) to yield weighted phase-aligned signal images WRx_(i)(t), which have substantially the same phase. System 210 adds the weighted phase-aligned signal images WRx_(i)(t) and normalizes the result to generate a combined signal output y(t), which is modified to generate correlation reference y′(t).

[0038] According to the illustrated embodiment, system 210 receives signals that are sampled as signal images x_(i)(t) defined by Equation (1):

x _(i)(t)=α_(i) d(t)+n _(i)(t)  (1)

[0039] where i corresponds to a signal branch 40 a, d(t) represents a signal, α_(i) represents a complex branch gain, and n_(i)(t) represents noise, where each noise term n_(i)(t) is mutually uncorrelated and uncorrelated relative to the signal d(t). Signal d(t) may comprise a phase-shift keying (PSK) signal, and noise n_(i)(t) may comprise additive white Gaussian noise (AWGN).

[0040] Each channel branch 235 a-b receives signal images x_(i)(t) and generates weighted phase-aligned signal images WRx_(i)(t) from the signal images. Each channel branch 235 a-b includes a phase aligner 241 a-b, a magnitude estimator 243 a-b, a weight calculator 260 a-b, and scalar multipliers 262 a-b and 266 a-b. Phase aligner 241 a-b includes multipliers 222 a-b and 226 a-b and phase-locked loop (PLL) circuits 224 a-b. Complex multipliers 222 a-b correlate signal images x_(i)(t) with a correlation reference y′(t) to yield phasors r_(i). An expression for combined signal output y(t), which may substantially represent correlation reference y′(t), may be given by Equation (2): $\begin{matrix} {{y(t)} = {\frac{1}{\sum\limits_{i}{W_{i}M_{i}}}{\sum\limits_{i}\left\lbrack {{W_{i}{\alpha_{i}}{d^{*}(t)}} + {W_{i}R_{i}^{*}{n_{i}^{*}(t)}}} \right\rbrack}}} & (2) \end{matrix}$

[0041] The correlation of signal images x_(i)(t) with the correlation reference y′(t) may remove modulation, since d*(t)d(t)=1.

[0042] Phase-locked loop circuits 224 a-b perform tracking and filtering to yield known magnitude phasors R_(i) having frequencies and phases that match the frequencies of phasors r_(i) or track the phases of phasors r_(i). A phase-locked loop circuit 224 a-b may comprise a complex multiplier 250 a-b, a numerically controlled oscillator (NCO) 256 a-b, and a loop filter 254 a-b. Complex multiplier 250 a-b correlates unity magnitude phasor R_(i) with phasor r_(i) to drive the imaginary component e_(i) of phasor r_(i) to zero and to resolve the real component m_(i) of phasor r_(i). The real component m_(i) may be used to represent the magnitude of phasor r_(i) by tracking the magnitude of the signal content α_(i)d(t) embedded in signal image x_(i)(t).

[0043] According to one embodiment, a numerically controlled oscillator 256 a-b comprises a perfect integrator coupled to a complex sinusoid generator such that the output frequency is proportional to the input drive. According to the embodiment, a loop filter 252 a-b comprises an imperfect integrator and a feed-forward path. A loop filter 252 a-b, along with an NCO 256 a-b, determines the type of phase-locked loop realized. Complex multipliers 226 a-b apply unity magnitude phasors R_(i) to signal images x_(i)(t), adjusting the phase alignment of α_(i)d(t) embedded in x_(i)(t), to yield adjusted signal images Rx_(i)(t). The signal images are phase aligned to support phase coherent constructive addition to generate combined signal output y(t).

[0044] Magnitude estimators 243 a-b include estimation filters 228 a-b that generate signal magnitude estimates M_(i) from real components m_(i). Signal magnitude estimates M_(i) provide an estimate of the signal content of signal images x_(i)(t). An estimation filter 228 a-b may comprise, for example, a narrow low pass filter to reduce the variance of the estimate. A real component m_(i) may be based on the stationary ergodic processes of signal image x_(i)(t), so the signal magnitude estimate M_(i) may provide an accurate estimate of the signal content |α_(i)d(t)| of signal image x_(i)(t).

[0045] Expressions (3) through (6) provide an explanation of the estimation process for determining signal magnitude estimate M_(i). Expressions (3) through (6) assume that coefficient K₁ is set to a value close to unity, such that correlation reference y′(t) substantially comprises combined signal output y(t).

[0046] Equation (3) defines phasor r_(i): $\begin{matrix} {r_{1} = {{{x_{1}(t)}{y(t)}} = {\left\lbrack {{\alpha_{1}{d(t)}} + {n_{1}(t)}} \right\rbrack \left\lbrack \frac{\sum\limits_{i}\left\lbrack {{W_{i}{\alpha_{i}}{d^{*}(t)}} + {W_{i}R_{i}^{*}{n_{i}^{*}(t)}}} \right\rbrack}{\sum\limits_{i}{W_{i}M_{i}}} \right\rbrack}}} & (3) \end{matrix}$

[0047] Expanding Equation (3) yields Equation (4): $\begin{matrix} {r_{1} = {{\alpha_{1}{d(t)}{d^{*}(t)}\frac{1}{\sum\limits_{i}{W_{i}M_{i}}}{\sum\limits_{i}{W_{i}{\alpha_{i}}}}} + {\alpha_{1}{d(t)}\frac{1}{\sum\limits_{i}{W_{i}M_{i}}}{\sum{W_{i}R_{i}^{*}{n_{i}^{*}(t)}}}} + {{n_{1}(t)}\frac{1}{\sum\limits_{i}{W_{i}M_{i}}}{d^{*}(t)}{\sum\limits_{i}{W_{i}{\alpha_{i}}}}} + {{n_{1}(t)}\frac{1}{\sum\limits_{i}{W_{i}M_{i}}}{\sum\limits_{i}{W_{i}R_{i}{n_{i}^{*}(t)}}}}}} & (4) \end{matrix}$

[0048] The uncorrelated terms of Equation (4) average to zero at estimation filter 228, resulting in the following relationship described by Equation (5): $\begin{matrix} {M_{1} \cong {E\left\lbrack m_{1} \right\rbrack} \cong {E\left\lbrack {r_{1}} \right\rbrack} \cong {{\alpha_{1}} + {\frac{W_{1}}{\sum\limits_{i}{W_{i}M_{i}}}{n_{1}(t)}R_{i}^{*}{n_{i}^{*}(t)}}}} & (5) \end{matrix}$

[0049] If the signal-to-noise ratio is high, the noise component n₁(t) is low, and if the signal-to-noise ratio is low, weight W₁ is very low. In either situation, the noise-cross-noise term is sufficiently small to substantially ignore. Therefore, the signal magnitude estimates M_(i) may be described by Equation (6).

M ₁≅|α₁ d(t)|, or generally M _(i)≅|α_(i) d(t)|  (6)

[0050] Sum-weight module 230 determines weights W_(i) applicable to signal images x_(i)(t) from signal magnitude estimates M_(i). Each weight W_(i) reflects the signal-to-noise ratio associated with the corresponding signal image x_(i)(t). Within sum-weight module 230, weights W_(i) are applied to phase-aligned signal images to yield weighted phase-aligned signal images. Sum-weight module 230 combines the weighted phase-aligned signal images and normalizes the result to generate the combined signal output y(t), which is modified to yield correlation reference y′(t).

[0051] Weight calculators 260 a-b calculate weights W_(i) from signal magnitude estimates M_(i). According to classical theory, maximal-ratio combining requires that signal images x_(i)(t) be weighted in accordance with S/N² and that {E[|x_(i)(t)|]}=C is maintained by the automatic gain control. Accordingly, E[n₁ ²(t)]=C²−M₁ ². As a result, in general the weights W_(i) may given by Equation (7): $\begin{matrix} {W_{i} = \frac{M_{i}}{C^{2} - M_{i}^{2}}} & (7) \end{matrix}$

[0052] Scalar multipliers 262 a-b apply weights W_(i) to adjusted signal images Rx_(i)(t) to generate weighted adjusted signal images WRx_(i)(t). A summing node 264 combines the weighted adjusted signal images WRx_(i)(t) to yield weighted sum Sum_(A)(t). The signal component of weighted sum Sum_(A)(t) may be defined by Equation (8): $\begin{matrix} {{{\sum\limits_{i}{W_{i}R_{i}\alpha_{i}{d(t)}}}} = {\sum\limits_{i}{W_{i}M_{i}}}} & (8) \end{matrix}$

[0053] Multipliers 266 a-b apply weights W_(i) to signal magnitude estimates M_(i) to yield weighted signal magnitude estimates WM_(i).

[0054] A normalizer circuit 271 substantially maintains the embedded signal energy of correlation reference y′(t) at unity. Normalizer circuit 271 comprises an adder 268, a multiplicative inverter 270, and a dual scalar multiplier 272. Summing node 268 combines the weighted signal magnitude estimates WM_(i). Multiplicative inverter 270 inverts the combined weighted signal magnitude estimates WM_(i) to yield a normalization factor G_(out), which may be defined by Equation (9): $\begin{matrix} {G_{out} = \frac{1}{\sum\limits_{i}{W_{i}M_{i}}}} & (9) \end{matrix}$

[0055] Multiplier 272 normalizes signal component of weighted sum Sum_(A)(t) to unity by applying normalization factor G_(out) to weighted sum Sum_(A)(t). In the final expression, |Rα_(i)|=|α_(i)|, and combined signal output y(t) may be described by Equation (10): $\begin{matrix} {{y(t)} = {\frac{\sum\limits_{i}{W_{i}R_{i}{x_{i}(t)}}}{\sum\limits_{i}{W_{i}M_{i}}} = {\frac{1}{\sum\limits_{i}{W_{i}M_{i}}}{\sum\limits_{i}{\left\lbrack {{W_{i}{\alpha_{i}}{d^{*}(t)}} + {W_{i}R_{i}{n_{i}^{*}(t)}}} \right\rbrack.}}}}} & (10) \end{matrix}$

[0056] Carrier recovery loop 233 drives phase-locked loop circuits 224 a-b to resolve the combined signal output y(t) to baseband, that is, zero frequency error. Carrier recovery loop 233 includes a collective phase detector 231 and a loop filter 232 that derive a phase error measurement, which may be applied to phase-locked loop circuits 224 a-b. Carrier recovery loop 233 may have, for example, a second order Type-II topology.

[0057] Modifications, additions, or omissions may be made to system 210 without departing from the scope of the invention. For example, a carrier recovery loop may be employed outside of system 210, such that carrier recovery loop 233 may be omitted. Carrier recovery loop 233 is not required to achieve phase alignment of signal images x_(i)(t), estimation of signal magnitude estimates M_(i), determination of weights W_(i), or normalization. Additionally, functions may be performed using any suitable logic comprising software, hardware, other logic, or any suitable combination of the preceding.

[0058]FIG. 4 is a block diagram illustrating one embodiment of reference constructor 72 of system 10 of FIG. 1. Reference constructor 72 combines adjusted signal images Rx_(i)(t) in accordance with magnitude estimates M_(i) to generate a correlation reference y′(t).

[0059] Reference constructor 72 includes branch reference constructors 310 a-b, a composite reference constructor 312, and a selector 314 coupled as shown in FIG. 5. Branch reference constructor 310 a generates a correlation reference from the signals received at frequency branch 22 a, and branch reference constructor 310 b generates a correlation reference from frequency branch 22 b.

[0060] According to one embodiment, branch reference constructor 310 a includes adders 320 a-b and 322, an amplitude normalizer 324, and multipliers 326 a-b. Adders 320 a-b add adjusted signal images Rx_(i)(t) generated from signals at receiver channels 50 a-b. Adder 322 adds magnitude estimates M_(i) from receiver channels 50 a-b. Amplitude normalizer 324 normalizes the sum of the magnitude estimates M_(i). Multipliers 326 a-b multiply the normalized sum of the magnitude estimates M_(i) with the sum of the adjusted signal images Rx_(i)(t) from receiver channels 50 a-b, respectively, to yield correlation references for receiver channels 50 a-b, respectively. Branch reference constructor 310 b may be substantially similar to branch reference constructor 310 a.

[0061] Composite reference constructor 312 generates a composite correlation reference from signals received at frequency branches 22 a-b. Composite reference constructor 312 includes adders 330 and 322 a-b, an amplitude normalizer 334, and multipliers 336 a-b. Adder 330 adds the sum of the signal magnitude estimates M_(i) from receiver channels 50 a-b with the sum of the signal magnitude estimates M_(i) from receiver channels 50 c-d to yield a combined signal magnitude estimate.

[0062] Adders 322 a-b add the sum of the adjusted signal images Rx_(i)(t) from receiver channels 50 a-b with the sum of adjusted signal images Rx_(i)(t) from receiver channels 50 c-d to yield combined adjusted signal images. Amplitude normalizer 334 normalizes the amplitude of the combined signal magnitude estimate. Multipliers 336 a-b multiply the combined adjusted signal image with the combined signal magnitude estimate.

[0063] Selector 314 selects the result of branch reference constructor 310 a, branch reference constructor 310 b, or composite reference constructor 312 in order to generate correlation reference y′(t). The selection may be made in accordance with the signal energies at the frequency branches 22 a-b. For example, if frequency branch 22 a has acquired a signal, but frequency branch 22 b has not acquired a signal, the correlation reference may derived using the signals from frequency branch 22 a. If frequency branches 22 a-b have acquired signals, the correlation reference may derived using the signals from frequency branches 22 a-b. The contribution of each frequency branch 22 a-b may be determined with respect to signal-to-noise-ratios at the frequency branches 22 a-b.

[0064] Modifications, additions, or omissions may be made to reference constructor 72 without departing from the scope of the invention. For example, reference constructor 72 may include more or fewer branch reference constructors 310. Additionally, functions may be performed using any suitable logic comprising software, hardware, other logic, or any suitable combination of the preceding.

[0065]FIG. 5 is a block diagram of one embodiment of coordinating modules 24 of system 10 of FIG. 1. Coordinating modules 24 monitor the correlation among signals from frequency branches 22 a-b, and provide instructions to interpolators 52 a-b to delay the signals in order to correlate the signals.

[0066] In general, coordinating modules 24 perform an initial correlating procedure to initially correlate the signals, and then perform a dynamic correlating procedure to perform subsequent adjustment. For purposes of illustration only, it is assumed that the samples from the signals of frequency branch 22 a are used as reference samples with which the samples from the signals from the signals of frequency branch 22 b are to be correlated.

[0067] Coordinating modules 24 include symbol aligner 60, correlator 62, and correlation monitor 64. Symbol aligner 60 includes a delay sweep control 410, an integrator 412, a multiplexer (MUX) 414, and a loop filter 416. In general, delay sweep control 410 sets a range of delays that is applied to the signals during the initial correlation procedure, and loop filter 416 dynamically adjusts the delay during the subsequent dynamic correlation procedure. Multiplexer 414 switches between delay sweep control 410 and loop filter 416 depending on the procedure.

[0068] According to one embodiment, delay sweep control 410 sets a range of delays during an initial correlating procedure by providing initial values for interpolators 52 a. The delay range may have any suitable range such as plus or minus four symbols. The initial values may comprise values for pointer value τ and phase φ. Delay sweep control 410 sends a square wave through multiplexer 414 to integrator 412. In response, integrator 414 produces a triangular ramp that results in the desired delay range. The sweep is continued until the signals are correlated.

[0069] This invention is not dependent on any specific triangular shape of the sweep function, and is not dependent on any method of generating a triangular sweep function. Other embodiments of this invention may employ, for example, a sinusoidal sweep function generated by any suitable mathematical or heuristic method that causes the delay of the interpolator delay line to vary over the desired range of time offset.

[0070] Loop filter 416 dynamically adjusts the delay during a subsequent dynamic correlation procedure. The dynamic correlation procedure is initiated if correlation monitor 64 detects signal decorrelation. Correlator 62 generates correlation information comprising a symbol alignment tracking error, which is provided to symbol aligner 60. Loop filter 416 receives the correlation information and sends instructions to interpolators 52 b in response to the information. The instructions may comprise a pointer value, which may be calculated according to correlation values that indicate the degree of signal correlation. Signals may be determined to be correlated if the correlation values satisfy a particular correlation threshold. A pointer value may comprise a value corresponding to the centroid of the correlation distributions satisfying the threshold, or may comprise a value corresponding to the midpoint between an initial correlation value satisfying a threshold and a final correlation value satisfying a threshold. Other criteria may be used to determine the delay associated with the best correlation.

[0071] In operation, according to the illustrated embodiment, frequency branch 22 a acquires a signal. Frequency branch 22 a provides samples from the signal to correlator 62 to be used as reference samples with which samples of frequency branch 22 b are to be correlated. The pointer value τ and the phase φ for interpolators 52 a of frequency branch 22 a are set to initial values to designate a delay range.

[0072] Frequency branch 22 b acquires a signal and provides samples from the signal to correlator 62. Interpolators 52 b of frequency branch 22 b sweep over the delay range. Correlator 62 monitors symbol alignment to generate correlation information. If the symbols align, multiplexer 414 switches control of interpolators 52 b to loop filter 416. Loop filter 416 dynamically controls interpolators 52 b in response to correlation information received from correlator 62.

[0073] Modifications, additions, or omissions may be made to the system without departing from the scope of the invention. Additionally, functions may be performed using any suitable logic comprising software, hardware, other logic, or any suitable combination of the preceding.

[0074] Certain embodiments of the invention may provide one or more technical advantages. A technical advantage of one embodiment may be that signals are combined in accordance with the signal-to-noise ratios associated with the signals, such that maximal ratio combining gain may be substantially realized. Accordingly, signals that exhibit multiple types of diversity such as temporal, frequency, polar, or spatial diversity may be combined.

[0075] Although the present invention has been described in several embodiments, various changes and modifications may be suggested to one skilled in the art. It is intended that the present invention encompass such changes and modifications as fall within the scope of the appended claims. 

What is claimed is:
 1. A method for combining a plurality of signals, comprising: receiving a plurality of signals comprising a plurality of first signals having a first frequency and a plurality of second signals having a second frequency; determining a first weight for each first signal of the first signals, the first weight reflecting a signal-to-noise ratio associated with the each first signal; generating a first signal output from the first signals in accordance with the first weights; determining a second weight for each second signal of the second signals, the second weight reflecting a signal-to-noise ratio associated with the each second signal; generating a second signal output from the second signals in accordance with the second weights; and combining the first signal output and the second signal output to yield a combined signal output.
 2. The method of claim 1, further comprising: determining a symbol offset among at least two signals, each signal of the signals comprising a plurality of symbols, the symbol offset describing an offset between the symbols of the at least two signals; and correlating the at least two signals in accordance with the symbol offset.
 3. The method of claim 1, wherein determining the first weight for each first signal of the first signals, the first weight reflecting the signal-to-noise ratio associated with the first signal comprises: establishing a signal magnitude estimate in accordance with a correlation reference; and determining a weight for the signal in accordance with the signal magnitude estimate.
 4. The method of claim 1, wherein receiving the signals comprises: receiving the signals at a first antenna and a second antenna, the first antenna and the second antenna separated by a distance; determining an offset among at least two signals; and correlating the at least two signals in accordance with the offset.
 5. The method of claim 1, wherein receiving the signals comprises: receiving the signals at a first antenna and a second antenna, the first antenna having a first polarization, the second antenna having a second polarization, the first polarization orthogonal to the second polarization; determining an offset among at least two signals; and correlating the at least two signals in accordance with the offset.
 6. A system for combining a plurality of signals, comprising: a first frequency branch operable to receive a plurality of signals comprising a plurality of first signals having a first frequency; a second frequency branch operable to receive the signals comprising a plurality of second signals having a second frequency; and a sum module coupled to the first frequency branch and the second frequency branch and operable to: determine a first weight for each first signal of the first signals, the first weight reflecting a signal-to-noise ratio associated with the each first signal; generate a first signal output from the first signals in accordance with the first weights; determine a second weight for each second signal of the second signals, the second weight reflecting a signal-to-noise ratio associated with the each second signal; generate a second signal output from the second signals in accordance with the second weights; and combine the first signal output and the second signal output to yield a combined signal output.
 7. The system of claim 6, wherein the first frequency branch is further operable to: determine a symbol offset among at least two signals, each signal of the signals comprising a plurality of symbols, the symbol offset describing an offset between the symbols of the at least two signals; and correlate the at least two signals in accordance with the symbol offset.
 8. The system of claim 6, wherein the sum module is operable to determine the first weight for each first signal of the first signals, the first weight reflecting the signal-to-noise ratio associated with the first signal by: establishing a signal magnitude estimate in accordance with a correlation reference; and determining a weight for the signal in accordance with the signal magnitude estimate.
 9. The system of claim 6, further comprising: a first antenna coupled to the first frequency branch and the second frequency branch and operable to receive the signals; and a second antenna coupled to the first frequency branch and the second frequency branch and operable to receive the signals, the first antenna and the second antenna separated by a distance, the first frequency branch operable to: determine an offset among at least two signals; and correlate the at least two signals in accordance with the offset.
 10. The system of claim 6, further comprising: a first antenna coupled to the first frequency branch and the second frequency branch and operable to receive the signals; and a second antenna coupled to the first frequency branch and the second frequency branch and operable to receive the signals, the first antenna having a first polarization, the second antenna having a second polarization, the first polarization orthogonal to the second polarization, the first frequency branch operable to: determine an offset among at least two signals; and correlate the at least two signals in accordance with the offset.
 11. Logic for combining a plurality of signals, the logic embodied in a medium and operable to: receive a plurality of signals comprising a plurality of first signals having a first frequency and a plurality of second signals having a second frequency; determine a first weight for each first signal of the first signals, the first weight reflecting a signal-to-noise ratio associated with the each first signal; generate a first signal output from the first signals in accordance with the first weights; determine a second weight for each second signal of the second signals, the second weight reflecting a signal-to-noise ratio associated with the each second signal; generate a second signal output from the second signals in accordance with the second weights; and combine the first signal output and the second signal output to yield a combined signal output.
 12. The logic of claim 11, further operable to: determine a symbol offset among at least two signals, each signal of the signals comprising a plurality of symbols, the symbol offset describing an offset between the symbols of the at least two signals; and correlate the at least two signals in accordance with the symbol offset.
 13. The logic of claim 11, operable to determine the first weight for each first signal of the first signals, the first weight reflecting the signal-to-noise ratio associated with the first signal by: establishing a signal magnitude estimate in accordance with a correlation reference; and determining a weight for the signal in accordance with the signal magnitude estimate.
 14. The logic of claim 11, operable to receive the signals by: receiving the signals at a first antenna and a second antenna, the first antenna and the second antenna separated by a distance; determining an offset among at least two signals; and correlating the at least two signals in accordance with the offset.
 15. The logic of claim 11, operable to receive the signals by: receiving the signals at a first antenna and a second antenna, the first antenna having a first polarization, the second antenna having a second polarization, the first polarization orthogonal to the second polarization; determining an offset among at least two signals; and correlating the at least two signals in accordance with the offset.
 16. A system for combining a plurality of signals, comprising: means for receiving a plurality of signals comprising a plurality of first signals having a first frequency and a plurality of second signals having a second frequency; means for determining a first weight for each first signal of the first signals, the first weight reflecting a signal-to-noise ratio associated with the each first signal; means for generating a first signal output from the first signals in accordance with the first weights; means for determining a second weight for each second signal of the second signals, the second weight reflecting a signal-to-noise ratio associated with the each second signal; means for generating a second signal output from the second signals in accordance with the second weights; and means for combining the first signal output and the second signal output to yield a combined signal output.
 17. A method for combining a plurality of signals, comprising: receiving a plurality of signals comprising a plurality of first signals having a first frequency and a plurality of second signals having a second frequency by receiving the signals at a first antenna and a second antenna, the first antenna and the second antenna separated by a distance, the first antenna having a first polarization, the second antenna having a second polarization, the first polarization orthogonal to the second polarization, by determining an offset among at least two signals, and by correlating the at least two signals in accordance with the offset; determining a symbol offset among at least two signals, each signal of the signals comprising a plurality of symbols' the symbol offset describing an offset between the symbols of the at least two signals, and correlating the at least two signals in accordance with the symbol offset; determining a first weight for each first signal of the first signals, the first weight reflecting a signal-to-noise ratio associated with the each first signal by establishing a signal magnitude estimate in accordance with a correlation reference, and determining a weight for the signal in accordance with the signal magnitude estimate; generating a first signal output from the first signals in accordance with the first weights; determining a second weight for each second signal of the second signals, the second weight reflecting a signal-to-noise ratio associated with the each second signal; generating a second signal output from the second signals in accordance with the second weights; and combining the first signal output and the second signal output to yield a combined signal output.
 18. A method for correlating a plurality of signals, comprising: receiving a plurality of signals at a filter, the filter having a plurality of phases, each phase associated with a weight correlation set; receiving correlation information associated with the signals, the correlation information describing a correlation among the signals; determining a phase associated with the signals in response to the correlation information; selecting a weight correlation set in accordance with the phase; and applying the selected weight correlation set to the signals to delay the signals in order to substantially correlate the signals.
 19. The method of claim 18, wherein applying the selected weight correlation set to the signals to delay the signals in order to substantially correlate the signals comprises: determining a pointer value associated with the signals in response to the correlation information; and applying the selected weight correlation set to the signals in accordance with the pointer value.
 20. The method of claim 18, further comprising: receiving an initial phase and an initial pointer value corresponding to a range of delays; and applying the range of delays to the signals in accordance with the initial phase and the initial pointer value.
 21. The method of claim 18, further comprising: determining an initial phase and an initial pointer value corresponding to a range of delays, the range of delays applied to the signals; monitoring the correlation among the signals through the range of delays; determining that the signals are correlated; and initiating a dynamic adjustment procedure in response to the determination.
 22. The method of claim 18, further comprising: monitoring the correlation among the signals to generate a plurality of correlation values; determining that the signals are not correlated; and calculating a next pointer value in accordance with the correlation values.
 23. A system for correlating a plurality of signals, comprising: a delay line operable to store a plurality of signals at a filter, the filter having a plurality of phases, each phase associated with a weight correlation set; and a processor operable to: receive correlation information associated with the signals, the correlation information describing a correlation among the signals; determine a phase associated with the signals in response to the correlation information; select a weight correlation set in accordance with the phase; and apply the selected weight correlation set to the signals to delay the signals in order to substantially correlate the signals.
 24. The system of claim 23, wherein the processor is operable to apply the selected weight correlation set to the signals to delay the signals in order to substantially correlate the signals by: determining a pointer value associated with the signals in response to the correlation information; and applying the selected weight correlation set to the signals in accordance with the pointer value.
 25. The system of claim 23, wherein the processor is further operable to: receive an initial phase and an initial pointer value corresponding to a range of delays; and apply the range of delays to the signals in accordance with the initial phase and the initial pointer value.
 26. The system of claim 23, further comprising a coordinating module operable to: determine an initial phase and an initial pointer value corresponding to a range of delays, the range of delays applied to the signals; monitor the correlation among the signals through the range of delays; determine that the signals are correlated; and initiate a dynamic adjustment procedure in response to the determination.
 27. The system of claim 23, further comprising a coordinating module operable to: monitor the correlation among the signals to generate a plurality of correlation values; determine that the signals are not correlated; and calculate a next pointer value in accordance with the correlation values.
 28. Logic for correlating a plurality of signals, the logic embodied in a medium and operable to: receive a plurality of signals at a filter, the filter having a plurality of phases, each phase associated with a weight correlation set; receive correlation information associated with the signals, the correlation information describing a correlation among the signals; determine a phase associated with the signals in response to the correlation information; select a weight correlation set in accordance with the phase; and apply the selected weight correlation set to the signals to delay the signals in order to substantially correlate the signals.
 29. The logic of claim 28, operable to apply the selected weight correlation set to the signals to delay the signals in order to substantially correlate the signals by: determining a pointer value associated with the signals in response to the correlation information; and applying the selected weight correlation set to the signals in accordance with the pointer value.
 30. The logic of claim 28, further operable to: receive an initial phase and an initial pointer value corresponding to a range of delays; and apply the range of delays to the signals in accordance with the initial phase and the initial pointer value.
 31. The logic of claim 28, further operable to: determine an initial phase and an initial pointer value corresponding to a range of delays, the range of delays applied to the signals; monitor the correlation among the signals through the range of delays; determine that the signals are correlated; and initiate a dynamic adjustment procedure in response to the determination.
 32. The logic of claim 28, further operable to: monitor the correlation among the signals to generate a plurality of correlation values; determine that the signals are not correlated; and calculate a next pointer value in accordance with the correlation values.
 33. A system for correlating a plurality of signals, comprising: means for receiving a plurality of signals at a filter, the filter having a plurality of phases, each phase associated with a weight correlation set; means for receiving correlation information associated with the signals, the correlation information describing a correlation among the signals; means for determining a phase associated with the signals in response to the correlation information; means for selecting a weight correlation set in accordance with the phase; and means for applying the selected weight correlation set to the signals to delay the signals in order to substantially correlate the signals.
 34. A system for correlating a plurality of signals, comprising: an interpolator operable to: receive a plurality of signals at a filter, the filter having a plurality of phases, each phase associated with a weight correlation set; receive an initial phase and an initial pointer value corresponding to a range of delays, and applying the range of delays to the signals in accordance with the initial phase and the initial pointer value; receive correlation information associated with the signals, the correlation information describing a correlation among the signals; determine a phase associated with the signals in response to the correlation information; select a weight correlation set in accordance with the phase; and apply the selected weight correlation set to the signals to delay the signals in order to substantially correlate the signals by determining a pointer value associated with the signals in response to the correlation information, and by applying the selected weight correlation set to the signals in accordance with the pointer value; and a coordinating module coupled to the interpolator and operable to: determine the initial phase and the initial pointer value corresponding to the range of delays, monitor the correlation among the signals through the range of delays, determine that the signals are correlated, and initiate a dynamic adjustment procedure in response to the determination; and monitor the correlation among the signals to generate a plurality of correlation values, determine that the signals are not correlated, and calculate a next pointer value in accordance with the correlation values.
 35. A method for generating a correlation reference, comprising: receiving a plurality of first signals having a first frequency; receiving a plurality of second signals having a second frequency; calculating a first correlation reference from the first signals; calculating a second correlation reference from the second signals; calculating a composite correlation reference from the first signals and the second signals; and generating a resulting correlation reference in accordance with a correlation reference selected from the set consisting of the first correlation reference, the second correlation reference, and the composite correlation reference.
 36. The method of claim 35, wherein calculating the first correlation reference from the first signals comprises: estimating a plurality of signal magnitude estimates according to the first signals, each signal magnitude estimate associated with a first signal; and calculating the first correlation reference according to the signal magnitude estimates.
 37. The method of claim 35, wherein calculating the first correlation reference from the first signals comprises: adjusting a phase alignment of the first signals to yield a plurality of adjusted signals; estimating a plurality of signal magnitude estimates according to the first signals, each signal magnitude estimate associated with a first signal; and calculating the first correlation reference according to the adjusted signals and the signal magnitude estimates.
 38. The method of claim 35, wherein calculating the first correlation reference from the first signals comprises: determining a signal energy associated with each first signal of the first signals; determining a contribution of each first signal in accordance with the determined signal energies; and calculating the first correlation reference in accordance with the determined contributions.
 39. The method of claim 35, wherein generating the resulting correlation reference in accordance with a correlation reference selected from the set consisting of the first correlation reference, the second correlation reference, and the composite correlation reference comprises: determining a first signal energy associated with the first correlation reference; determining a second signal energy associated with the second correlation reference; and selecting the resulting correlation reference from the first correlation reference, the second correlation reference, and the composite correlation reference in accordance with the first signal energy and the second signal energy.
 40. A system for generating a correlation reference, comprising: a first branch reference constructor operable to calculate a first correlation reference from a plurality of first signals having a first frequency; a second branch reference constructor operable to calculate a second correlation reference from a plurality of second signals having a second frequency; and a composite reference constructor operable to calculate a composite correlation reference from the first signals and the second signals; and a selector coupled to the first branch reference constructor, the second branch reference constructor, and the composite reference constructor and operable to generate a resulting correlation reference in accordance with a correlation reference selected from the set consisting of the first correlation reference, the second correlation reference, and the composite correlation reference.
 41. The system of claim 40, wherein the first branch reference constructor is operable to calculate the first correlation reference from the first signals by: estimating a plurality of signal magnitude estimates according to the first signals, each signal magnitude estimate associated with a first signal; and calculating the first correlation reference according to the signal magnitude estimates.
 42. The system of claim 40, wherein the first branch reference constructor is operable to calculate the first correlation reference from the first signals by: adjusting a phase alignment of the first signals to yield a plurality of adjusted signals; estimating a plurality of signal magnitude estimates according to the first signals, each signal magnitude estimate associated with a first signal; and calculating the first correlation reference according to the adjusted signals and the signal magnitude estimates.
 43. The system of claim 40, wherein the first branch reference constructor is operable to calculate the first correlation reference from the first signals by: determining a signal energy associated with each first signal of the first signals; determining a contribution of each first signal in accordance with the determined signal energies; and calculating the first correlation reference in accordance with the determined contributions.
 44. The system of claim 40, wherein the selector is operable to generate a resulting correlation reference in accordance with a correlation reference selected from the set consisting of the first correlation reference, the second correlation reference, and the composite correlation reference by: determining a first signal energy associated with the first correlation reference; determining a second signal energy associated with the second correlation reference; and selecting the resulting correlation reference from the first correlation reference, the second correlation reference, and the composite correlation reference in accordance with the first signal energy and the second signal energy.
 45. Logic for generating a correlation reference, the logic embodied in a medium and operable to: receive a plurality of first signals having a first frequency; receive a plurality of second signals having a second frequency; calculate a first correlation reference from the first signals; calculate a second correlation reference from the second signals; calculate a composite correlation reference from the first signals and the second signals; and generate a resulting correlation reference in accordance with a correlation reference selected from the set consisting of the first correlation reference, the second correlation reference, and the composite correlation reference.
 46. The logic of claim 45, operable to calculate the first correlation reference from the first signals by: estimating a plurality of signal magnitude estimates according to the first signals, each signal magnitude estimate associated with a first signal; and calculating the first correlation reference according to the signal magnitude estimates.
 47. The logic of claim 45, operable to calculate the first correlation reference from the first signals by: adjusting a phase alignment of the first signals to yield a plurality of adjusted signals; estimating a plurality of signal magnitude estimates according to the first signals, each signal magnitude estimate associated with a first signal; and calculating the first correlation reference according to the adjusted signals and the signal magnitude estimates.
 48. The logic of claim 45, operable to calculate the first correlation reference from the first signals by: determining a signal energy associated with each first signal of the first signals; determining a contribution of each first signal in accordance with the determined signal energies; and calculating the first correlation reference in accordance with the determined contributions.
 49. The logic of claim 45, operable to generate the resulting correlation reference in accordance with a correlation reference selected from the set consisting of the first correlation reference, the second correlation reference, and the composite correlation reference by: determining a first signal energy associated with the first correlation reference; determining a second signal energy associated with the second correlation reference; and selecting the resulting correlation reference from the first correlation reference, the second correlation reference, and the composite correlation reference in accordance with the first signal energy and the second signal energy.
 50. A system for generating a correlation reference, comprising: means for receiving a plurality of first signals having a first frequency; means for receiving a plurality of second signals having a second frequency; means for calculating a first correlation reference from the first signals; means for calculating a second correlation reference from the second signals; means for calculating a composite correlation reference from the first signals and the second signals; and means for generating a resulting correlation reference in accordance with a correlation reference selected from the set consisting of the first correlation reference, the second correlation reference, and the composite correlation reference.
 51. A method for generating a correlation reference, comprising: receiving a plurality of first signals having a first frequency, and receiving a plurality of second signals having a second frequency; calculating a first correlation reference from the first signals by: adjusting a phase alignment of the first signals to yield a plurality of adjusted signals, estimating a plurality of signal magnitude estimates according to the first signals, each signal magnitude estimate associated with a first signal, and calculating the first correlation reference according to the adjusted signals and the signal magnitude estimates; estimating a plurality of signal magnitude estimates according to the first signals, each signal magnitude estimate associated with a first signal, and calculating the first correlation reference according to the signal magnitude estimates; and determining a signal energy associated with each first signal of the first signals, determining a contribution of each first signal in accordance with the determined signal energies, and calculating the first correlation reference in accordance with the determined contributions; calculating a second correlation reference from the second signals; calculating a composite correlation reference from the first signals and the second signals; and generating a resulting correlation reference in accordance with a correlation reference selected from the set consisting of the first correlation reference, the second correlation reference, and the composite correlation reference by determining a first signal energy associated with the first correlation reference, by determining a second signal energy associated with the second correlation reference, and by selecting the resulting correlation reference from the first correlation reference, the second correlation reference, and the composite correlation reference in accordance with the first signal energy and the second signal energy. 